Understanding the Tangent of 45 Degrees | Definition, Calculation, and Value

tan45

The tangent of 45 degrees, denoted as tan(45), is the mathematical function that gives the ratio of the length of the side opposite to the angle of 45 degrees in a right triangle to the length of the side adjacent to the angle

The tangent of 45 degrees, denoted as tan(45), is the mathematical function that gives the ratio of the length of the side opposite to the angle of 45 degrees in a right triangle to the length of the side adjacent to the angle. In simpler terms, it represents the slope or inclination of a line that makes an angle of 45 degrees with the positive x-axis.

To calculate the value of tan(45), we can consider a right triangle with one of its angles measuring 45 degrees. By convention, we often use a right triangle with side lengths of 1 unit. In this case, the side opposite the angle of 45 degrees and the side adjacent to it will have equal lengths.

Using the Pythagorean theorem, we can find the length of the hypotenuse (the longest side) by applying the formula:

c^2 = a^2 + b^2

Substituting the values, we have:

c^2 = 1^2 + 1^2
c^2 = 2
c ≈ √2

So, the hypotenuse has a length approximately equal to the square root of 2 (√2).

Now, to find the value of tan(45), we simply divide the length of the side opposite the angle by the length of the side adjacent to it:

tan(45) = (opposite side)/(adjacent side)
= 1/1
= 1

Therefore, tan(45) equals 1.

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